Can a woman get an orgasm from a routine pelvic examination?

Not Likely. Most women have some difficulty having an orgasm under ideal circumstances. A routine pelvic exam is not intended to be arousing. It is possible for some women to become aroused by the combination of being undressed and in a submissive vulnerable position, but an orgasm would be very unlikely. If you are attracted to your doctor to the point of arousal, it may be better for you to change doctors.
No. The setting and the way the exam are done makes this extremely unlikely.